A recent addition to

http://groups.yahoo.com/group/primeform/files/GenLuc/luctop.txt
benefitted from Satoshi Tomabechi's SNFS.

> prime digs who Cmin F1 F2 proof

> lucasU(5621,-1,1801) 6750 x25 117 0.1786 0.1666 WL

was missing 80 digits to achieve the Williams-Lenstra threshold

F1+F3>1/3. In N-1 there was a C90 with a neat quartic representation:

C90 = primU(5621,-1,45) = x^4+x^3-4*x^2-4*x+1

x = 1+primU(5621,-1,9) = 31541445621788159525778

which Satoshi's beta version factored in under 7 hours

on an 1GHz Athlon:

===== data of factorization by NFS =====

polynomial (x^4+x^3-4*x^2-4*x+1) x=31541445621788159525778

[factor base]

RFB 22190 AFB 16985 QCB 28

FF FP PF PP PPF

9577 21888 45226 102100 45845 7873 36993 102402 5512

#free-rel 4246

large prime upper bound 5118638 3667837

36356 relations by LPV

sieve region |a| < 39424 b < 78350

[reduction of square]

reduced square 13 digit 349 iteration

square root 7 digit

embedding : ln(abs(\prod(a+b\theta)))

initial 1642.89 2408.59 1301.75 1633.35

final 1.37421 2.95243 1.43862 -1.38182

[block Lanczos method]

#trial 1 #pseudo dependencies 29 #real dependencies 29

final matrix 38337*37991 5753K

#nonzero entry 1472548 38.7604/row

[trial]

#dependencies 65156 trial 1 severe error 0

[factor]

103589852304634507491928934924568241 *

9554526362492897852956064429176725960566683505187322321

[cputime] 6:48:58:94

(sieve 6:22:04:51

LPV 0:02:08:46

construct matrix 0:05:04:09

Lanczos 0:03:21:27

Lanczos All 0:03:21:27

productR 0:00:37:34

productA 0:02:40:31

LLL reduction 0:02:23:88

reduced square 0:00:00:08

ideal decomposition 0:00:03:43

Hensel lift 0:00:00:06)

Square All 0:08:32:69

It can be seen that the sieve takes 90% of the time,

so I am itching for Satoshi to upgrade it using the

methods that Kida has implemented for quintics.

The final phases, which contain the smart Montgomery

math, went very quickly.

Ohkini, Satoshi!

David